Graphene synthesis on single crystal Rh(1 1 1) catalytic substrates is performed by Chemical Vapor Deposition (CVD) at 1000 degrees C and atmospheric pressure. Raman analysis shows full substrate coverage with few layer graphene. It is found that the cool-down rate strongly affects the graphene stacking order. When lowered, the percentage of AB (Bernal)-stacked regions increases, leading to an almost full AB stacking order. When increased, the percentage of AB-stacked graphene regions decreases to a point where almost a full non AB-stacked graphene is grown. For a slow cool-down rate, graphene with AB stacking order and good epitaxial orientation with the substrate is achieved. This is indicated mainly by Raman characterization and confirmed by Reflection high-energy electron diffraction (RHEED) imaging. Additional Scanning Tunneling Microscopy (STM) topography data confirm that the grown graphene is mainly an AB-stacked structure. The electronic structure of the graphene/Rh(1 1 1) system is examined by Angle resolved Photo-Emission Spectroscopy (ARPES), where sigma and pi bands of graphene, are observed. Graphene's Gamma K direction is aligned with the Gamma K direction of the substrate, indicating no significant contribution from rotated domains. (C) 2016 Elsevier B.V. All rights reserved.